Methods and Systems for Generating Continuous Surfaces from Polygonal Data

1. A method of producing BREP data from electronic polygonal data, the method comprising: accessing the polygonal data with a computer, the polygonal data defining a mesh of polygonal data points, each having a valence corresponding with the number of polygons defined thereby, wherein the data points comprise: a plurality of valence four data points having a valence of four, and a plurality of non-valence four data points having a valence other than four; selecting one or more of the non-valence four data points, wherein the selected non-valence four data points are selected at least partly on the basis of having a valence other than four; generating a plurality of continuous curves based on the polygonal data; identifying a plurality of first data points corresponding to non-valence 4 vertices in the polygonal data; identifying a plurality of second data points corresponding to polygonal data having a third derivative greater than a threshold; based at least in part on the continuous curves, the first data points, and the second data points, generating a plurality of BREP surface boundaries defining one or more continuous BREP surfaces, wherein each of the continuous BREP surface boundaries terminates on one of the selected non-valence four data points and passes through one or more particular valence four data points; generating the BREP data based at least in part on the continuous BREP surfaces; generating one or more additional continuous surfaces, each additional surface being generated based on points corresponding to vertices in the polygonal data which are near one of the non-valence 4 vertices corresponding to an identified non-valence 4 data point, wherein at least one of the additional continuous surfaces terminates at at least one of the second data points; improving the continuity of the BREP data using the continuous additional surfaces; and storing the improved BREP data in a computer readable data storage.

2. The method of claim 1 , wherein the continuous curves include the points of the mesh.

3. The method of claim 1 , wherein the continuous curves are G2 continuous.

4. The method of claim 1 , wherein the BREP surface boundaries intersect one or more of the curves.

5. The method of claim 1 , wherein the surface boundaries are G2 continuous at points corresponding to valence 4 vertices in the polygonal data.

6. The method of claim 1 , wherein improving the continuity of the BREP data comprises modifying an identified first data point based on one of the additional continuous surfaces.

7. The method of claim 1 , wherein improving the continuity of the BREP data comprises adding a plurality of knots to the BREP data based on one of the additional continuous surfaces.

8. The method of claim 1 , wherein generating the BREP surface boundaries comprises extending surface boundary segments from the identified first data points.

9. The method of claim 1 , wherein generating the BREP surface boundaries comprises extending surface boundary segments from the second data points.

10. The method of claim 1 , wherein each first vertex having valence n corresponds to a point on the BREP surface boundary of n of the continuous BREP surfaces, wherein n is an integer.

11. A method of producing BREP data from electronic polygonal data, the method comprising: accessing the polygonal data with a computer, the polygonal data defining a mesh of polygonal data points, each having a valence corresponding with the number of polygons defined thereby, wherein the data points comprise: a plurality of valence four data points having a valence of four, and a plurality of non-valence four data points having a valence other than four; selecting one or more of the non-valence four data points, wherein the selected non-valence four data points are selected at least partly on the basis of having a valence other than four; identifying a plurality of high curvature data points, each identified high curvature data point corresponding to a non-valence 4 vertex in the polygonal data; identifying a plurality of second data points corresponding to polygonal data having a third derivative greater than a threshold; generating a plurality of BREP surface boundaries defining one or more continuous BREP surfaces, wherein each of the continuous BREP surface boundaries terminates on one of the selected non-valence four data points and passes through one or more particular valence four data points; generating one or more continuous surfaces, each generated surface being generated based on points corresponding to vertices in the polygonal data which are near one of the non-valence 4 vertices corresponding to an identified data point, wherein at least one of the one or more continuous surfaces terminates at at least one of the second data points; identifying a plurality of second data points corresponding to polygonal data having a third derivative greater than a threshold; generating the BREP data based at least in part on the continuous surfaces and the second data points; improving the continuity of the BREP data using the continuous surface; and storing the BREP data in a computer readable data storage.

12. The method of claim 11 , wherein each continuous surface is G2 continuous.

13. The method of claim 11 , wherein each continuous surface is generated based on points corresponding to vertices which are adjacent to the corresponding non-valence 4 vertex.

14. The method of claim 11 , wherein each continuous surface is generated based on points corresponding to vertices which substantially surround the corresponding non-valence 4 vertex.

15. The method of claim 11 , wherein improving the continuity of the BREP data comprises modifying each identified point based on the corresponding continuous surface.

16. The method of claim 12 , wherein modifying each identified point comprises projecting the identified point onto the corresponding continuous surface at a projection point.

17. The method of claim 16 , wherein each continuous surface is normal to the corresponding identified point at the projection point.

18. The method of claim 11 , wherein improving the continuity of the BREP data comprises adding a plurality of knots to the BREP data based on each continuous surface.

19. The method of claim 18 , wherein improving the continuity of the BREP data comprises modifying each identified point based on the corresponding continuous surface, and wherein the knots are added between each modified point and other points corresponding to adjacent points.

20. The method of claim 18 , wherein the plurality of surface boundaries define one or more additional continuous surfaces, wherein generating the BREP data is based at least in part on the additional surfaces, and wherein the knots are added on the additional surfaces.

21. The method of claim 20 , further comprising improving the continuity of the knots added on the boundaries defining the additional surfaces.

22. The method of claim 21 , wherein improving the continuity of the knots added on the boundaries comprises: generating a continuous curve on each of the additional surfaces which share a boundary, wherein each continuous curve on each additional surface includes knots added on the surface and has an added knot on the shared boundary as an end point; determining a tangent for each of the added knots on each curve, wherein the added knot on the shared boundary has a first tangent from a first curve on a first additional surface and a second tangent from a second curve on a second additional surface; modifying the first and second tangents so as to be parallel; and regenerating the first and second additional surfaces based at least in part on the added knots and the tangents of the added knots.

23. The method of claim 11 , further comprising generating a plurality of surface boundaries defining one or more additional continuous surfaces, wherein the identified points correspond to points on the surface boundaries.